How does power output relate to frequency transmitted?

I am trying to build a radio receiver, but I am not sure whether to build a ULF, ELF, or VLF, because I am not sure of the frequency I am trying to receive.

I only have the money to build one of these (if someone has a circuit diagram for a receiver that accepts all of these wavelengths, they would be the best!).

I've been doing a lot of research, but still have some questions.

1.) How does power output relate to the frequency of transmitted waves? Does a lower power relate to lower frequency transmission capacity?

2.) Is there a way to increase a 402 Mhz signal so that it travels over 5000 miles? Is there a way to increase the distance waves travel at all?

3.) Which wavelength frequencies travel farther, Low Frequency (20-20000hz) or High Frequency (20000 hz and higher) at a LOW POWER (>1 uA) output?

4.) How does antenna length relate to wave distance traveled? Is it possible that a very small antenna (1mm) at low power (>1 uA) can transmit waves over 5000 miles? What frequency range would the waves transmitted fall in?

Thanks!

Consult the amatuer radio league lots of sites out thier they will be able to assist you in these questions

I am not a radio expert but will try to explain using simple terms:

Power and frequency are not directly related - frequency determines the size of the radiator (i.e., antenna) while power dictates how long the signal will travel before being attenuated down to useless levels. Somewhat like brightness and colour - you can have a very bright red light that can be seen from afar, but a rather dim blue that cannot be seen from from afar (despite the fact that blue light has a much higher frequency than red). This is of course a very simplistic explanation since depending on frequency (its range, to be correct) the signal can use either the earth's surface or the atmosphere (ozone layer, especially) as a sort of reflector to increase the range. The former behaviour is typical of LW broadcast range and the latter of SW broadcast range. MW range signals are neither here not there. Note that the terms LW/MW/SW are user-friendly terms and must not be confused with the actual ranges: VLF, LF, HF, VHF, UHF, SHF and so on.

Some frequency ranges are such that they are line-of-sight only - VHF/UHF (i.e. those used for FM or TV transmissions) typically fall into this range.

Discover which radio stations can be received in your geographical area.

Discover the transmitting frequencies of the available radio stations you want to receive.

Then you will know the waveband (range of frequencies) that your radio needs to process.
(E.g. Long Wave, Medium Wave, Short Wave, Very High Frequency; SW, MW, LW, VHF)

In some areas, radio stations can be received on more that one waveband, so your receiver can be built to receive two or three wavebands.

Google:
Radio receiver project
Radio receiver circuit diagram